New methods for the efficient optimization of cumulant-based contrast functions

This paper deals with efficient optimization of the cumulant-based contrast functions. Such a problem occurs in the blind source separation framework, where contrast functions are criteria to be maximized to retrieve the sources. Inspired from the recently proposed reference contrast functions, a similar one called new kurtosis contrast function is put forward. Based on this criterion, new efficient optimization methods are proposed. They are similar in spirit to the classical algorithms based on the kurtosis contrast function, but differ in the fact that they show a cubic dependence with respect to the searched parameters. Therefore, the main advantage of these new methods consists in the significant improvement of computational speed, which is particularly striking with large number of samples. Simulations validate the performance of these methods and also show experimentally that they are much quicker than some classical and other corresponding methods.